Core-annular flow (CAF) through a pipe is characterized by a fluid or mixture disposed at the center or core of the flow, known as the core region, and a relatively low viscosity fluid or mixture disposed about the core region between the core region and the walls of the pipe, known as the annular region. A phenomenon associated with CAF is that the lower viscosity annular region naturally migrates to the high sheer region found at the wall of the pipe where it acts to levitate the core region off of the pipe wall and lubricate the flow.
One example of CAF is found in the oilsands processing industry, where bitumen is extracted from mined oilsand as bitumen froth using a hot water extraction process. Bitumen is the primary component in bitumen froth, which typically contains about 50–60% bitumen, about 30–40% water, and about 10% fine solids and clays. The challenge in transporting bitumen through pipelines is derived from its high static viscosity, on the order of 105 times that of water at standard conditions. If bitumen froth behaved as a Newtonian fluid, i.e. the shear stress was strictly proportional to shear rate, pumping bitumen froth would require several orders of magnitude more power than that required to pump water, rendering pipeline transfer impractical.
Fortunately, bitumen froth is a shear thinning fluid. The viscosity of these types of non-Newtonian fluids decreases with increasing shear rate. Shear thinning fluids tend to exhibit CAF regimes, in which the motion of the fluid through the pipe set ups an essentially rigid, core region in the center of the pipe, surrounded by a highly-sheared, less-viscous annular region which effectively lubricates the core flow. From an operational perspective, the primary result of this self-lubrication of bitumen froth (often termed Natural Froth Lubricity or NFL) is a significant reduction (several orders of magnitude) in the pressure drop required to pump a given amount of bitumen froth compared to that predicted by a model using the static viscosity and Newtonian model of the fluid rheology.
Another example of the application of CAF is found in the so-called core-annular lubricated pipelining of oil, where a fluid such as water is added to the flow of oil to create a CAF with the oil forming the core region and the water forming the annular region. Water lubricated pipelining was applied, for example, in the 24 mile long pipeline from North Midway Sunset Reservoir near Bakersfield, Calif., to the central facilities at Ten Section. In this pipeline, oil was lubricated by water (including sodium at about 0.6 wt %) at a volume flow rate of 30% of the total. It is reported that CAF was stable as long as the flow velocity was at least 0.9 meters per second.
The CAF regime of bitumen froth and core-annular lubricated oil flow are described in articles entitled “Steady Flow and Interfacial Shapes of a Highly Viscous Dispersed Phase, by Runyuan Bai, Daniel D. Joseph, in International Journal of Multiphase Flow (2000), vol. 26, pp. 1469–1491; “Self-Lubricated Transport of Bitumen Froth” by Daniel Joesph, Runyan Bai, Clara Mata, Ken Sury, Chris Grant, in J. Fluid Mech. (1999), vol. 286, pp. 127–148; and “Multiphase Pipelining”, by Daniel Joseph, in Proposal to the Department of Energy, Office of Basic Energy Sciences, Division of Engineering, December 2000, all of which are incorporated herein by reference.
Another example of the application of CAF is found in the paper pulp industry, which relies on large-diameter-pipe conveyed slurries to transport pulp throughout the process of papermaking. It has been recognized that the suspension flow behavior of wood pulp fiber is directly related to the flocculation tendency of the constituent fibers. The entanglement of fibers and subsequent floc formation and development of fiber networks gives fiber suspensions unique flow mechanisms not encountered in other particulate solid suspensions.
Fiber suspension flow can be characterized broadly by three different flow regimes: plug flow, transition flow, and turbulent flow. Each regime can be further divided into subregimes with well-defined shear mechanisms. There are four major regimes of plug flow. At the lowest flow rates, friction loss is independent of velocity, and fiber-plug-wall (solid-solid) friction dominates. As flow rate increases, the shear rate is sufficient to force the protruding flocs back into the plug surface to produce a smoother plug. In so doing, a CAF develops wherein a water annular region in laminar shear develops around the fiber plug core region, and the friction loss decreases. As small scale turbulence in the thin peripheral layer onsets, shear stresses begin removing the fibers from the plug permanently. The transition from plug flow to turbulent flow starts as the plug diminishes in size and a turbulent fiber-floc-water annular region develops. Pipe friction loss is reduced further below water alone. The point of maximum drag reduction is reached in the transition flow regime where a fiber plug core region approximately 20% of the pipe diameter still exists. The suspension finally reaches fully developed turbulence where there is no central plug.
The characteristics of this type of CAF is described in the following articles, which are incorporated herein by reference; “Modeling Fiber Flocculation in Turbulent Flow: a numerical Study” by Morten Steen, September 1991 Tappi Journal, pp. 175–182; “Characterization of Pulp Suspensions”, by Robert Powell, Sitram Ramaswamy, Matthew Weldon, Michael McCarthy, 1996 Engineering Conference, pp. 525–533; “New Insights into the Flow of Pulp Suspensions”, by Torsten Paul, Geoff Duffy, Dong Chen, 2001 Tappi Peer-Reviewed Paper, Sept 2001 vol1: No. 1; “Pressure Loss and Velocity Profile of Pulp Flow in a Circular Pipe”, by Kohei Ogawa, Shiro Yoshikawa, Jun Ikeda, Hirohisa Ogawa, April 1990 Tappi Juornal, pp. 217–221.
Historically, obtaining accurate and reliable measurements of CAF has proven technically difficult and economically challenging. Firstly, CAF flows may be extremely abrasive. For example, some bitumen froth flows contain >50% solids by mass with particle distributions ranging from several microns up to several inches in diameter. These flows typically exhibit some level of stratification, as evidenced by the preferential wear of the lower portion of the pipelines in which they are transported, requiring the pipes to be rotated on a periodic basis. The presence of ˜10% by volume of non-conductive bitumen further complicates the flow measurement, as does the possibility of the pipe containing up to several percent of entrained air by volume.
Currently, modified venturi (or wedge) meters are the predominant devices used to measure flow rates in pipelines transporting CAF. Mechanical wear of these meters results in high maintenance, calibration, and replacement costs, providing an incentive for operators to evaluate alternative measurement technologies.
In addition, these meters are invasive. That is, they are installed such that they extend through piping into contact with the fluid in the flow process. As a result, installation or maintenance of the meter often requires at least a portion of the flow process to be isolated. Therefore, it is desirable to have a meter that is easily installed.
One attempt to measure velocity profiles of wood pulp suspensions through pipe using a non-invasive method is described Tie-Quiang Li, et al., in “Velocity measurements of fiber suspensions in pipe flow by the nuclear magnetic resonance imaging method”, Tappi Journal Vol. 77, No. 3. As implied by its title, this paper describes the application of nuclear magnetic resonance imaging (NMRI) to observe the flow of cellulose fiber suspensions in pipes. While the use of NMRI was shown to be successful in characterizing velocity, the use of NMRI equipment may be economically challenging for many applications.
Thus, there remains a need for a convenient and economical apparatus for obtaining accurate, and reliable measurements of the characteristics of CAF.